Polarization molar

The dipole moment per unit volume of the dielectric is made up of contributions from all the molecules in the unit volume. If N is the number of molecules per unit volume, and m is the average dipole moment per molecule induced by the field, then the dipole moment per unit volume is mN  

If a molecule that has no permanent dipole moment is placed in an electrical field, the electronic cloud will be displaced slightly toward the positive plate. This distorted molecule possesses a dipole moment m, which is proportional to the applied field. 

The constant of proportionality ocq is the distortion polarizability of the molecule. The polarizability is the dipole moment produced by an applied field of unit strength. 

The field that acts on a molecule in the dielectric is so that m = aE y. Using this value for m in Eq. (26.10) and rearranging, we obtain 

Since N = p/M, where p is the density and M the molar mass of the substance, we can write this equation in the form 

---

The quantity on the left side of the equation is called the molar polarization, and this expression is the Clausius—Mosotti equation. On the right side the quantity a is the polarizability, which measures the ease with which an induced moment is... 

The connection between the molar polarization Pm and the molar refraction Rm is through Maxwell s theory of electromagnetism, according to which e = (at low-frequency fields). This is the basis for considering the molar refraction a measure of polarizability. 

The linear response of a medium to a weak applied electric field is characterized by the dielectric constant <0. From this experiment we deduce the molar polarization mP which is related to the mean square dipole moment by... 

Sastry, N.V., George, A., Jain, N.J., and Bahadur, P. Densities, relative permittivities, excess volumes, and excess molar polarizations for alkyl ester (methyl propanoate, methyl butanoate, ethyl propanoate, and ethyl butanoate) + hydrocarbons (n-heptane, benzene, chlorobenzene, and 1,1,2,2-tetrachloroethane) at 308.15 and 318.15 K, J. Chem. Eng. Data, 44(3) 456-464, 1999. 

If this argument is applied to two permanent dipoles, the polarizability may be regarded as the sum of two contributions one that is independent of the presence of the permanent dipole a0 and a second that is the average effect of the rotation of the molecules in the electric field. The molar polarization P of a substance is given by... 

In examining the Debye, Keesom, and London equations we see that (a) they share as a common feature an inverse sixth-power dependence on the separation and (b) the molecular parameters that describe the polarization of a molecule, polarizability and dipole moment, serve as proportionality factors in these expressions. For a full discussion of the experimental determination of a0 and p, a textbook of physical chemistry should be consulted (Atkins 1994). For our purposes, it is sufficient to note that the molar polarization of a substance can be related to its relative dielectric constant e, by... 

The molar polarization of the solvent, P, is given by the Clausius-Mosotti expression P = V(s - l)/(s + 2), similar to the expression for the molar refraction. It is the molar polarization that relates the relative permittivity to the dipole moment p and the polarizability a ... 

The molar refraction RD and molar polarization P per unit volume, i.e., the functions f (nD) = ( D -1)/ + 2) and g(e) = (s -l)/(s + 2), or similar functions with 1 replacing 2 and/or 2 multiplying nD and s in the denominators, have often been employed in correlations of chemical properties of solvents with their physical, optical, and electrical properties. 

Debye-Clausius-Mossotti equation -> Debye expanded the - Clausius-Mossotti equation and related the molar polarization P with the -> dielectric constant er, the electron polarizability a of an individual molecule, and the - dipole moment p P = nN0 a + = f Vm... 

Molar polarization - Debye-Clausius-Mossotti equation... 

This is the Clausius-Mossotti equation. The quantity Pm is called the molar polarization and has the dimensions of volume per mole. 

Measurements in Solution. We are concerned here with a dilute solution containing a polar solute 2 in a nonpolar solvent 1. The molar polarization can be written... 

Thus measurements on solutions of the slope of k versus X2 and the slope of p versus X2 enable us to calculate the limiting molar polarization of the solute in solution. If we assume that the molar distortion polarization in an infinitely dilute solution is equal to that in the pure solute, then... 

For each solution studied, calculate k from Eq. (30) as well as p and X2. Plot k and p versus the mole fraction of solute X2, and draw the best straight lines through your points see Eqs. (18) and (19). Obtain the slopes a and b, the intercepts should agree with the pure solvent results. Using Eq. (20), calculate F2M, the molar polarization at infinite dilution. Estimate from Eq. (21) using the literature value of the refractive index of the solute / 2, and obtain... 

The permanent dipole moment /tt of a polar molecule is determined in Exp. 29 from measurements of the dielectric constant of a solution containing such molecules as solute. In the present experiment, the permanent dipole moment of a gas molecule is determined. The orientation polarization can be separated from the distortion polarization by means of measurements at more than one temperature, making use of the fact that the former is temperature dependent while the latter is not. An alternative method, which is recommended for this experiment, is to obtain the orientation polarization by subtracting from the molar polarization the distortion polarization as determined separately from the refractive index of the gas, which is determined by means of a laser interferometer. Thus the molar polarization needs to be determined at only one temperature. 

The concepts of permanent dipole moment, induced dipole moment, and molar polarization are discussed in Exp. 29 this material should be reviewed. We assume further that deviations from the perfect-gas law are small in comparison with the experimental uncertainties. 

Schematic representation of the frequency dependence of the molar polarization of a gas of permanent dipoles. Dashed lines indicate ranges of complex behavior.

The molar polarization of these gases may be regarded as independent of temperature, and K - may be considered to be proportional to the density of the gas. Thus, at temperatures and pressures other than 293.2 K and 1 atm, assuming the perfect-gas law,... 

Number of phases, power, scalar polarization Molar polarization... 

Provided that the field-induced non-linearity is not too large, the preceding formula yields, tvith regard to the definition (2A6) and equation (250), the following quadratic variation of the molar polarization ... 

In the case now under consideration, we make use of the distribution functions in the form of the expansion (100) with the potential energy (188). This leads to the following quadratic change in molar polarization ... 

This relation, together wth definition (246) and equation (309b), leads to the following non-linear diange in molar polarization ... 

The other part of the molar polarization (240) is, in Kirkwood s theory, of the following form ... 

By insertine the mean dipole moment (2S2a) into the polarization fonnula (2S1) and using the definitions (246) and (2S0), one obtains the change in molar polarization of a gas due to the square of the electric field strength ... 

---